FR2751811A1 - DIGITAL DEMODULATION PROCESS - Google Patents

Abstract

A receiver device (120) performs N distinct demodulations (N> = 2) each providing respective estimates of successive binary symbols resulting from a differential coding of a sequence of bits transmitted by a transmitter device, said differential coding being of the form ak = ck <T 482> af (k) where ak and ck denote the binary symbol of rank k and the bit of rank k, f (k) denotes an integer at most equal to k-1 and <T 482> denotes l 'exclusive OR operation. Each estimate of a binary symbol of rank k is a real number sk ** (i) (1 = <i = <N) whose sign represents the most probable value of said symbol and whose modulus measures the likelihood of said value most likely. The value of a rank k bit of the sequence is estimated on the basis of the number: (CF DRAWING IN BOPI)

Description

DIGITAL DEMODULATION PROCESS

The present invention relates to a digital demodulation method. It applies in particular to a receiving device

implementing a reception diversity technique.

Diversity techniques are well known in the field of digital transmission. Among these techniques, mention may be made of: spatial diversity, which can be used in particular in radio transmission when several reception sensors are arranged at different locations; - frequency diversity when the same information is transmitted simultaneously on different frequencies; - temporal diversity in the event of repetition of the

same information.

These different diversity techniques can also be combined with one another. The advantage of these techniques is that they make it possible to improve the bit error rates in the estimates produced by the receiving device. On the other hand, they generally have the drawback of requiring additional resources, in terms of bandwidth and / or

complexity of transmitter and receiver devices.

To combine the multiple estimates obtained by the diversity receiver, there are many methods, among which one can quote: - the selection method consisting simply in choosing the observation having the best signal / noise ratio; the so-called "equal gain combining" method, in which a decision is taken from the sum of the observations after phasing; - the so-called "maximum ratio combining" method, in which a decision is taken from the sum of the squares of the observations phased and divided by the

estimated power of the noises with which they are affected.

The latter method provides a maximum signal-to-noise ratio after recombination. The observations available may not be subject to completely decorrelated disturbances (noise, channel) (especially with regard to the channel). In this case, conventional recombination methods do not obtain the expected results. Moreover, in digital transmissions, only the likelihood of observations and the resulting decision-making count, in the sense of maximum likelihood; this aspect

does not appear explicitly in the classical methods.

An aim of the present invention is to provide an alternative, based on the maximum likelihood, to the conventional methods of recombination of estimates.

affected by different disturbances.

The invention thus proposes a digital demodulation method, in which a receiving device performs N distinct demodulations (N> 2) each providing respective estimates of successive binary symbols ak resulting from a differential coding of a sequence of bits ck transmitted by a transmitter device, said differential coding being of the form ak = ck e af (k) o ak and ck denote the binary symbol of rank k and the bit of rank k, f (k) denotes an integer at most equal to k- 1 and e designates the exclusive OR operation, each estimate of a binary symbol ak of rank k being in the form of a real number sk) (li N) whose sign represents the most probable value of said symbol and whose modulus measures the likelihood of said most probable value. According to the invention, the receiving device estimates the value of a bit ck of rank k of the sequence on the basis of a number of the form Xk-Yk o: Xk = 1+ Sf (k) Y = max ls ( ) s (i) * H max {s (1) (i) * Yk =. <iN It is shown that, as soon as the level of the useful signal is sufficiently large with regard to that of the observation noise, the estimate Xk-Yk above is proportional to the likelihood of the bit ck, that is to say say to the logarithm of the ratio of the probability densities of the signal (s) received conditionally to the bit ck and

conditionally to the logical complement of bit Ck.

Global demodulation therefore obeys the rule of maximum a posteriori likelihood, even in the presence of correlated errors in the various estimates of

ak symbols.

The invention applies not only to the recombinations of multiple estimates obtained by a diversity technique, but also to the case where at least two of the N sets of estimates of the symbols ak are obtained by demodulating a same signal segment received by different methods (one case where, typically, the errors

estimate will often be correlated).

In a particular embodiment, at least two of the N distinct demodulations are performed on the same signal segment corresponding to a frame of symbols of a digital signal modulated by the transmitting device, said signal segment being received by the receiving device after transmission of the modulated digital signal via a transmission channel, the first of these two demodulations comprising the following steps: - estimation of first demodulation parameters at a first end of the segment; and - calculation of first estimates of symbols of the frame on the basis of the first estimated demodulation parameters and of the signal segment traveled from the first end to a second end, and the second of these two demodulations comprising the following steps: - estimation of second demodulation parameters at the second end of the segment; and - calculation of second estimates of symbols of the frame on the basis of the second estimated demodulation parameters and of the signal segment traveled since the second

end to the first end.

This way of proceeding leads to appreciable gains on the binary error rate, from a

only observation of the signal.

Other peculiarities and advantages of this

invention will appear in the following description

non-limiting exemplary embodiments, with reference to the appended drawings, in which: FIG. 1 is a block diagram showing a transmitter device and a receiver device implementing the present invention; FIG. 2 is a diagram showing the structure of signal frames in an exemplary embodiment of the present invention; FIGS. 3 and 4 are flowcharts of demodulation procedures applied by the receiving device in both directions of demodulation; FIG. 5 is a graph showing examples of likelihoods obtained in each direction of demodulation; FIG. 6 is a flowchart showing a way of combining the round trip estimates according to the invention; and - Figure 7 shows another embodiment

of a receiving device according to the invention.

The invention is described below in its application to digital radiocommunications between a transmitter device 10 and a receiver device 20. The transmitter device 10 comprises a source encoder 12 (a vocoder in the case of a telephone system) which delivers a digital data stream xk organized in successive frames. In the exemplary embodiment illustrated by FIG. 2, the signal xk is organized in frames of 126 bits at

a rate 1 / T = 8 kbit / s.

A channel encoder 14 processes the bits delivered by the source encoder to improve robustness to transmission errors. In the example of FIG. 2, the channel encoder 14 applies a CC (2,1, 3) convolutional code of rate 1/2 to the first 26 bits of the frame xk. The resulting 52 + 100 = 152 bits ek are then subjected to interleaving intended to break up the error packets that may be introduced by the phenomenon of Rayleigh fading. An 8-bit synchronization word is inserted after each frame of 152 interleaved information bits to form the signal ck that the encoder 14 sends to the modulator 16. The latter forms the radio signal s (t) which is amplified and then applied to l. antenna 18 of the transmitter device 10. In the example considered, the

ck symbols are binary (Ck = 0 or 1).

The modulation used is for example a GMSK modulation with a parameter BT = 0.25 (see K. MUROTA et al: "GMSK modulation for digital mobile radio telephony", IEEE Trans. On Communications, Vol. COM-29, N 7, July

1981, pages 1044-1050).

The receiver device 20 comprises a demodulator

24 receiving the signal picked up by the antenna 22 and amplified.

The demodulator 24 delivers estimates of the emitted symbols ck. These estimates are noted Sk in the case

soft decisions, and dk in the case of hard decisions.

If the symbols ck are M-ary and between 0 and M-1, a possible choice of representation for the soft estimate Sk is in the form: Sk = Pk- exP (2jdk / M), that is say that, in this case, its argument 2tdk / M represents the most probable value dk of the symbol Ck, while its modulus Pk is a measure of the likelihood of this value dk. In the case of binary symbols (M = 2),

the number Sk is real and called "softbit", and its sign 2dk-

1 directly gives the most probable value of the symbol

signed 2Ck-1.

The receiver device 20 comprises a dual channel decoder 26 of the channel 14 encoder of the transmitter. In the example previously considered, the channel decoder 26 operates frame by frame the reverse permutation of the bits corresponding to the interlacing applied by the transmitter, and decodes the 52 redundant bits using the Viterbi trellis corresponding to the convolutional code used . As is usual in digital transmissions, Viterbi decoding can be hard decision when demodulator 24 provides only dk, or soft decision when

the demodulator 24 supplies the Sk.

The channel decoder 26 restores the estimates Yk of the bits xk, and delivers them to a source decoder 28 which resets

forms the information transmitted.

As shown in Figure 1, the demodulator 24 comprises a radio stage 30 ensuring the baseband conversion of the received signal. By means of two mixers 32, 34, the received radio signal is mixed with two quadrature radio waves at the carrier frequency delivered by a local oscillator 36, and the resulting signals are subjected to low pass filters 38, 40 to obtain a in-phase component and a quadrature component. These two components are sampled and quantized by analog-to-digital converters 42, 44 at a frequency at least equal to the frequency of the transmitted bits. We denote by Rn the complex samples of the digital signal in band

base delivered by converters 42, 44.

In the example shown in FIG. 1, the demodulator 24 operates according to a sequential algorithm to demodulate binary symbols. In the case of GMSK modulation, sequential demodulation can be performed using the following approximation for the baseband modulated signal s (t): + k s (t) = E j. ak.h (t-kT) (4) k = -w This expression corresponds to a first order approximation of the decomposition proposed by PA LAURENT in his article "Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses ( AMP) ", IEEE Trans. on Communications, Vol. COM-34, n 2, February 1986, pages 150-160. This article also explains the method of calculating the function h (t), which, in the case of GMSK modulation with BT = 0.25, corresponds to a pulse of width 2T approximately centered on t = 0. In expression (4), the binary symbols ak, of value 1, correspond to the coded bits ck

differentially: ak = ak-l. (2Ck-l).

The radio channel is affected by fading corresponding to the sum of the multiple paths corresponding to the various reflections of the signal emitted on near or far obstacles. The temporal dispersion of these paths being usually of the order of 12 gs, a short duration compared to the duration of a bit (T = 125 gs in the digital example considered), the propagation channel is represented by a complex variable A ( t) corresponding to a Rayleigh attenuation and a phase shift with a single path. The frequency of fading is 2fd, fd being the Doppler frequency associated with the variation in the distance between the transmitter and the receiver: fd = fO.v / c, if f0 is the center frequency of the channel, v is the relative speed of the transmitter and the receiver and it is the speed of light. We then find for a speed of 100 km / h a Doppler frequency of the order of 41.67 Hz in the case of f0o450 MHz, hence a fading (83.33 Hz) every 12 ms. This therefore allows more than one fading per frame, and above all a fading frequency greater than the

frequency of synchronization words (50 Hz).

The presence of these rapid fading, and more generally the rapid variation of the channel compared to the duration of the frame, require a frequent estimation of the channel, and therefore a significant risk of propagation of errors due to the feedback of the decision loop. Indeed, in the event of errors on the binary symbols decided during the demodulation, these errors will lead to erroneous estimates of the channel, which will itself produce new

demodulation errors.

We denote by Ak = A (kT) (k = 0 to 167) the complex values of the propagation channel sampled at 8 kHz in baseband. The channel is also affected by an additive Gaussian white noise B (t) of variance N0 / 2, noted Bk after sampling and adapted filtering. The signal received, after suitable filtering of the signal by the response filter 46 h (t), is then of the form: Cc rk = A (kT) nja H ((nk) T) + B (kT) n = -o = Ak [jk-laklH (-Tb) + jkakH (0) + jk + lak + lH (+ T)] + Bk o H (t) is the known autocorrelation function of the function h (t). In this expression, we have made the approximation consisting in neglecting H (t) for | tl Ä 2T, this

which simplifies calculations.

The output samples rk of the matched filter 46 are stored in a memory 48 to be processed by the

controller 50 of demodulator 24.

The controller 50 processes the filtered signal rk by segments each corresponding to a frame of 168 transmitted binary symbols ak (0 k <168). As shown in figure 2,

this frame corresponds, after the implied differential coding

quotes from bits ck, to the 152 information bits of a frame framed by the 8 bits of the previous synchronization word

and by the 8 bits of the next synchronization word.

The controller 50 performs the demodulation according to a sequential algorithm, a first phase of which is shown in the flowchart of FIG. 3. In this first phase, one starts by estimating the complex response of the channel at the start of the segment, then this segment is demodulated. from start to finish by updating at each bit-time

estimation of the complex response of the channel.

At the initialization 60 of this first phase, the bits bA and bA are respectively taken equal to the symbols

known binaries a0 and a1, and the index k is initialized to 2.

In step 62, the index k is compared to 8, that is to say to the length of the synchronization word. If k <8, the bit b is taken equal to the known bit ak of the synchronization word in step 64, then one proceeds, in step 66, to an instantaneous estimate V_1 of the propagation channel, by performing the complex division : A rk-1 VA _rkl (5) k.1k-2A -k-1 A k bk2H (-T) + j + bklH (O) + j "bH (+ T) A filtering of the instantaneous estimates VA makes it possible to smooth the effects of the Gaussian noise to provide the estimate A4_1 used for the demodulation of the bits. In the example represented in FIG. 3, this filtering is simply the calculation of the arithmetic mean of the last six instantaneous estimates Vm. One could also use d 'other types of filtering After step 66, the index k is compared to 167 (the length of the frame) in step 68. As long as k <167, the index k is incremented by one.

unit to step 70 before returning to step 62.

The estimation of the channel at the start of the frame is terminated when k = 8 in test 62. The estimation AA obtained by virtue of the knowledge of the synchronization word is then available. For each value of k> 8, the softbit sA is estimated in step 72 according to: A = Re (rk.A k_2.jk (6) and the estimate bA of the bit ak is obtained by the sign of the softbit sk. Having obtained this bit bk, the controller 50 reestimates the channel at step 66 as explained previously. Demodulation in the forward direction is complete when k = 167

during test 68.

It can be seen in FIG. 3 that an error made on a bit bk in step 72, due for example to a fading of the channel or to an impulsive noise, causes distortions in the instantaneous estimates V _1, V and VA + 1 made in the following three steps 66, and thus leads to channel estimation errors which propagate for a certain time due to the smoothing filter. These mistakes in AA can in turn generate other mistakes.

bit estimation.

FIG. 5 thus shows, in the case where the signal received at an energy evolving along curve E in phantom (with channel fading occurring at time k0), that the likelihood I sj of the estimates (curve in dotted line ) is good before fainting, but then takes some time to regain values related

with the energy E of the received signal.

To improve performance in the post-fading period, the controller 50 performs another demodulation of the signal segment corresponding to the fading period.

168-bit frame from the end of the segment to the beginning.

This makes it possible to obtain likelihoods I sI such as those represented by the curve in solid lines in FIG. 5. It can be seen that the performance of the demodulator will be improved if the softbits sA are favored before

fainting and s4 softbits after fainting.

The reverse demodulation is carried out in a second phase similar to the first, the flowchart of which is shown in FIG. 4. In this second phase, we start by estimating the complex response of the channel at the end of the segment, then we demodulate this. segment from the end to the beginning by updating at each bit-time the estimate of

the complex response of the channel.

At the initialization 160 of this second phase, the bits b! 67 and bR66 are respectively taken equal to the known binary symbols a7 and a6, and the index k is initialized to 165. At step 162, the index k is compared to 159. If k> 159, the bit bR is taken equal to the known bit ak_160 of the synchronization word in step 164, then one proceeds, in step 166, to an instantaneous estimation VR + 1 of the propagation channel , by performing the complex division: VR k + l (7) k + 1 k + k + l RkR _ k + 2b H, + k + lbH (O) + j3 kH (-T) R k ++ T) + l Un filtering of the instantaneous estimates Vm makes it possible to smooth the effects of the Gaussian noise to provide the estimate A, + 1 used for the demodulation of the bits. In the example shown in FIG. 4, this filtering is simply the calculation of the arithmetic mean of the last six instantaneous estimates VR. After step 166, the index k is compared to 0 in step 168. As long as k> 0, the index k is decremented by one in step 170 before

go back to step 162.

The estimation of the channel at the end of the frame is finished when k = 159 in test 162. We then have the estimation A161 obtained thanks to the knowledge of the synchronization word. For each value of k 159, the softbit sR is estimated at step 172 according to: SR = Re (rk.Ak + 2.jk (8) and the estimate bR of the bit ak is obtained by the sign of the softbit s4. Having obtained this bit bk, controller 50

reestimates the channel at step 166 as discussed previously.

Demodulation in the return direction is complete when k = 0

during test 168.

In the example considered above, the demodulation parameters reestimated during the travel of the demodulated segment in each direction are limited to the complex response Ak of the propagation channel. It will be understood that they could include other parameters such as parameters representative of the noise observed on the transmission channel. It is thus possible to calculate for each direction of demodulation a quadratic mean of the deviations Vk_-A A (step 66) or VR + i-Ak + 1 (step 166), to estimate the instantaneous power of the noise N0A, N0O in each direction of demodulation. We can then normalize the value of the softbit sA or sR by dividing it by this quadratic mean. The power estimates N0A, N0R can be constant over the frame considered; these are then, for example, the averages of the A_ 1_- Vk_1 2 and of the 1 Aj + i- V + 1 j 2 calculated over the entire frame. If these averages are obtained on sliding windows or by filtering, the estimates

of the noise power can be instantaneous, i.e.

say depend on index k. Figure 6 shows a way of exploiting the round trip estimations of the transmitted symbols, by looking for the maximum a posteriori likelihood of the

value of transmitted bits.

The value of the softbit Sk obtained after differential decoding is then: Sk = Xk-Yk (9) o Xk = max {s_l + s, ISl + sR} (10) Yk = max {ISA-- sA 'IsR1SRI} (11)

as illustrated by steps 90 and 92 in FIG. 6.

The hard estimate dk of the bit ck is taken equal to [1 + sgn (Sk)] / 2 at step 88. These steps 90, 92, 98 are executed for each value of k between 8 and 159

A = Re (7.A * j-7.

(for the calculation of S8, we take s7 = Re (r7.A6.j7)).

Simulations have shown that, compared to a demodulation in one direction, a round trip demodulation combined with an exploitation of the results according to the maximum likelihood (figure 6) leads to an improvement of 1.5 to 2 dB on the binary error rate, with signals constructed in a manner analogous to what has been described with reference to FIG. 2 and current values of the Doppler frequency / bit frequency ratio. It is noted that the estimates Sk calculated in steps and 92 of FIG. 6 correspond to a maximum likelihood in the case where it can be considered that the observation noise is of the same power in both directions of demodulation, which, in practice , is generally a satisfactory approximation. If we do not make this approximation, it is advisable to normalize the softbits s, s relative to the noise power, as explained above, before calculating the maxima according to the relations

(10) and (11).

In the example considered above, the symbols ak depend on the bits ck by a differential encoding of the form ak = cke af (k), of (k) = k-1 and e designates the exclusive OR operation which, in the case where the ak are with values 1 and the ck with values 0 or 1, is equivalent to ak = (2ck-1) .af (k). In the general case, it suffices that the integer function f satisfies f (k)> k-1, the quantities Xk and Yk being Xk = max fs + Sf (k), 4s + S (k) (12) Yk = max ks S (k), sk - S (k)} When f (k) = k-1, relations (12) and (13) correspond to (10) and (11). An example of application of the differential coding o f (k) is not always equal to k- 1 can be found in the French patent application

13471.

FIG. 7 shows another example of a receiving device capable of implementing the present invention. This device 120 uses reception diversity which, in the example considered, is spatial diversity, the

device comprising n antennas 221, ..., 22n and n demodula-

associated teurs 241, ..., 24n. Each demodulator 24i operates in a single direction on a respective signal segment supplied by its antenna 22i, and delivers respective softbits s> i) (standardized or not) for each symbol ak before decoding

differential. The device 120 thus has N = n estimated

tions per symbol from different signal segments

rents, instead of N = 2 estimates from the same segment of

signal in the embodiment of Figures 1 to 6.

A module 25 combines these different softbits to provide the soft estimates Sk (and / or hard dk) of the decoded bits ck to the channel decoder 26. These combinations are made according to relation (9) with Xk = max {Is () + Sf ( k)} (14) Yk1 <7 <N k Sf (k) ik: max llS (k) - s ((i))} (15) The demodulation operated by each demodulator 24i is for example in accordance with the flowchart of FIG. 3, the signals received differing from one demodulator to another and being denoted rki) after adapted filtering, and the estimates bk of the bits ak in the forward direction which can be replaced

by the estimates bk of these same bits after recombination

his. After having obtained the respective softbits (ski) in step 72, the demodulators 24i supply these softbits to the combination module 25 which calculates the estimates Sk

and dk, then the bit bk by differential coding of the estimates

hard tions dk, i.e. bk = dke bf (k). The bit bk thus obtained is returned to the demodulators 24i which can then calculate the estimates V (i of the responses of the channels at step 72 according to: (i) (i) r k-1 Vk-l = k 'k' jk- 2 bk-2H (-T) + jk- lbk_ H (O) + jkbkH (+ T) The invention is of course applicable to other diversity techniques, or to receivers combining a diversity technique with a method of demodulations

multiples such as that described above.

Claims (9)

Method of digital demodulation, in which a receiving device (20; 120) performs N distinct demodulations (N> 2) each providing respective estimates of successive binary symbols (ak) resulting from a differential encoding of a sequence of bits (ck) transmitted by a sending device (10), said differential coding being of the form ak = ck e af (k) o ak and ck denote the binary symbol of rank k and the bit of rank k, f (k) denotes an integer at most equal to k-1 and e designates the exclusive OR operation, each estimate of a binary symbol (ak) of rank k being in the form of a real number s (i) (l1i N) whose sign represents the most probable value of said symbol and whose module measures the likelihood of said most probable value, characterized in that the receiving device (20; 120) estimates the value of a bit (ck) of rank k of the sequence based on a number of the form Xk-Yk o: = max is M + Sf (k) k max sk - (ky II i (i) I Yk kf (k 2. Method according to claim 1, characterized in that the receiving device (20) produces a hard estimate of each bit (ck) of rank k on the basis of the sign of the. Xk-Yk number. 3. Method according to claim 1 or 2, characterized in that at least two of the N distinct demodulations are performed on the same signal segment corresponding to a frame of symbols (ak) of a digital signal modulated by the transmitter device ( 10), said signal segment (r (t)) being received by the receiving device (20) after transmission of the modulated digital signal (s (t)) via a transmission channel, in that the first of these two demodulations comprises the following steps: - estimation of first demodulation parameters (AA) at a first end of the segment; and - calculation of first estimates (sA, bA) of symbols of the frame on the basis of the first estimated demodulation parameters and of the signal segment traveled from the first end to a second end, and in that the second of these two demodulations comprises the following steps: - estimation of second demodulation parameters (At) at the second end of the segment; and calculating second estimates (sR, bR) of symbols of the frame on the basis of the second estimated demodulation parameters and the signal segment traversed since the second end to the first end. 4. Method according to claim 3, characterized in that the first demodulation parameters are reestimated at least once during the course of the segment from the first end, and the second demodulation parameters are reestimated at least once during the route of the segment from the second end. 5. Method according to claim 3 or 4, characterized in that the first and second demodulation parameters each comprise at least one parameter (Ah, AR) representing the response of the transmission channel. A method according to claim 5, characterized in that the receiving device (20) estimates said parameters representing the response of the transmission channel at the ends of the segment on the basis of synchronization sequences included in the digital signal frames. 7. Method according to any one of claims 3 to 6, characterized in that the first and second demodulation parameters each comprise at least one parameter relating to the noise observed on the transmission channel. 8. Method according to claim 7, characterized in that the first demodulation parameters comprise the power of the noise whose estimate (N0O) is used to normalize the first estimates of the symbols of the frame, and in that the second parameters of demodulation include the power of the noise whose estimate (N0O) is used to normalize the second estimates of the frame symbols. 9. A method according to any one of claims i to 8, characterized in that at least two of the N distinct demodulations are performed on two respective signal segments, received by the receiving device (120) according to a diversity technique.